A fuzzy set analysis for a fracture and fatigue damage response of composite materials

Muc, Aleksander; Kędziora, Piotr

doi:10.1016/s0263-8223(01)00099-x

Cited by 20 publications

(12 citation statements)

References 5 publications

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“…The validity of the model should be also estimated by the inclusion of the uncertainties dealing with the shape of reinforcements or representative cells, e.g., using fuzzy sets [37]. …”

Section: Discussionmentioning

confidence: 99%

Design of Particulate-Reinforced Composite Materials

Muc

Barski

2018

Materials

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A microstructure-based model is developed to study the effective anisotropic properties (magnetic, dielectric or thermal) of two-phase particle-filled composites. The Green’s function technique and the effective field method are used to theoretically derive the homogenized (averaged) properties for a representative volume element containing isolated inclusion and infinite, chain-structured particles. Those results are compared with the finite element approximations conducted for the assumed representative volume element. In addition, the Maxwell–Garnett model is retrieved as a special case when particle interactions are not considered. We also give some information on the optimal design of the effective anisotropic properties taking into account the shape of magnetic particles.

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“…The validity of the model should be also estimated by the inclusion of the uncertainties dealing with the shape of reinforcements or representative cells, e.g., using fuzzy sets [37]. …”

Section: Discussionmentioning

confidence: 99%

Design of Particulate-Reinforced Composite Materials

Muc

Barski

2018

Materials

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“…The critical loading which leads to the further propagation of the existing delamination is estimated using the multiaxial fracture criterion (2). The critical lines for bi-axial compression and assumed geometrical propertiesh = 1.5 mm, a/ R = {2.67, 3.33, 4, 5.33} and layer orientation [0/ 908] are determined for RB del = 1 and presented in the diagram, Figure 14.…”

Section: Numerical Analysis Using Multiaxial Fracture Criterionmentioning

confidence: 99%

“…Because of this, many engineering structures have to be inspected to detect, control and locate often invisible fatigue damages before they lead to catastrophic failure. Due to this facts, the durability and the fatigue life estimation in a regime of cyclic loadings is an important issue [1][2][3].…”

Section: Introductionmentioning

confidence: 99%

“…In the first approach, which is based on the damage mechanics, the interface enclosing the internal damage is modeled using a damageable material [9,10]. The second technique, which is recently quite popular in the analysis of the damage growth in multilayered composite structures, is based on the fracture mechanics (FM) [2,3]. In fracture mechanics, the propagation of the damage can be investigated using the strain energy release rate parameter (SERR).…”

Section: Introductionmentioning

confidence: 99%

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Experimental and numerical estimation of the damage level in multilayered composite plates

Romanowicz

2018

Materialwissenschaft Werkst

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The detection of the internal and surface damage and estimation of the critical delamination size is discussed. The problem is illustrated on examples of glass/epoxy and graphite/epoxy composite plates. Experimental static and fatigue tensile tests were performed for multi‐layered plates with a circular hole and a circular delamination with the passive thermography and the digital image correlation used simultaneously for full‐field monitoring of thermal and mechanical effects. Both techniques are compared and verified in the context of detection and prediction of damage under static and fatigue loads. The technique of critical delamination size calculation is presented on the example of a plate made of a graphite/epoxy material. The computations were performed for bi‐axial compression using the finite element analysis and multiaxial fracture criteria. Different criteria are compared. It was observed that only nonlinear‐interaction criteria are suitable for the analysis of glass/epoxy and graphite/epoxy composite structures. It was also found that the mixed form of all three gap opening modes may occur in a composite plate with internal delamination. The proposed procedure for detection and analysis of damage is applicable in structural health monitoring of composite structures.

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“…Applying the vertex method only the interval bounds (in the one dimensional case) or corners (in the multi dimensional case) of the input α-level sets are taken into account. Nevertheless, numerous applications have been presented on this basis [17,20,21]. In the more general case that the solution can be determined investigating the edges of the input α-level sets a gradient method has been applied to solve differential equations containing fuzzy parameters [22].…”

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confidence: 99%

Uncertain structural design based on nonlinear fuzzy analysis

Beer

2004

Z Angew Math Mech

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In this paper a comprehensive application of fuzzy set theory in structural engineering is presented. Non-stochastic uncertainty is quantified using fuzzy values. The fuzzy structural parameters are processed on the basis of a generally applicable numerical method for arbitrary linear and nonlinear fuzzy structural analyses. This method is formulated in terms of α-level optimization combined with a modified evolution strategy. The fuzzy structural responses are compared with permissible values and assessed using an analog to the Shannon entropy and defuzzification algorithms. Referring to permissible fuzzy structural responses uncertain structural design parameters are derived by applying a fuzzy cluster analysis to the fuzzy structural parameters. The nonlinear fuzzy structural analysis including uncertain structural design is demonstrated by way of an example. Uncertainty in structural engineeringStructural engineering mainly focuses on computing structural responses, assessing structural safety, and determining parameters for structural design that meets all relevant requirements. For this purpose, the structural engineer has to apply appropriate structural models, suitably-matched computational models, and reliable structural parameters close to reality. Structural models and structural parameters have to be established on the basis of plans, drawings, measurements, observations, experiences, expert knowledge, codes, and standards. As a rule certain information regarding structural models and precise values of structural parameters do not exist. Computational models must be capable of numerically simulating the system behavior of the structural model chosen. Mathematically exact solutions, however, are only available in exceptional cases. In general, weak solutions and approximations are used, internal parameters, e.g. in material laws, have to be defined, and numerical solution techniques including lower bounds for numerical accuracy are applied. These facts show that structural engineering is significantly characterized by uncertainty. In order to perform realistic structural analysis and safety assessment this uncertainty must be appropriately taken into consideration.Different methods are available for mathematically describing and quantifying uncertainty. Some of these basic concepts are e.g. probability theory [1], including subjective probability approach [2] and Bayes methods [3], interval mathematics [4], convex modeling [5], theory of rough sets [6], fuzzy set theory [7], theory of fuzzy random variables [8], and chaos theory [9]. In the scientific literature the new uncertainty models are not only controversially discussed [10] but also increasingly implemented for the solution of practice-relevant problems [11][12][13][14][15][16][17][18]. These different developments of uncertainty models do not directly contradict each other but rather constitute an entirety.The choice of an appropriate uncertainty model for solving a particular problem depends on the characteristic of the uncertainty present in...

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A fuzzy set analysis for a fracture and fatigue damage response of composite materials

Cited by 20 publications

References 5 publications

Design of Particulate-Reinforced Composite Materials

Design of Particulate-Reinforced Composite Materials

Experimental and numerical estimation of the damage level in multilayered composite plates

Uncertain structural design based on nonlinear fuzzy analysis

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